Dynamics for an electromechanical integrated electrostatic harmonic drive

In this paper, an electromechanically coupled dynamic equation for an integrated electrostatic harmonic drive is presented. The dynamic equation is transformed into a balance equation for static displacement and a dynamic equation for dynamic displacement. The electromechanical-coupled force is considered as well. The operating principle for the drive system is analyzed. By defining the electromechanically coupled forces in Fourier series form, the static displacements of the ring are obtained. Changes in the voltage, along with ring displacement, are discussed. Using the same dynamic equation, the natural frequencies and mode functions of the drive system are given for a different electric field. The first natural frequency is influenced by the phase number of the electric field, but not by the pole pair number. Similarly, the second, third, and fourth natural frequencies are influenced both by pole pair number and by phase number. As radial displacement of the ring increases, the voltage will arrive at an extreme value where the flexible ring becomes buckled. For modes having higher natural frequencies, more positions of the dynamic peak displacements occur, and the time periods of the mode functions become shorter. Also, the pole pair number and phase number of the electric field exhibit an obvious influence on the positions of the dynamic peak displacements and time periods of the mode functions.